上面的方程是物理学中很重要的一类方程。许多研究者利用临界点理论知识，得

The above equation is a very important type of equation in physics. Many researchers use critical point theory knowledge to get a series of good solution existence results. We consider the existence results of the solution of f in subcritical, supercritical and critical situations.

The above equation is an important class of equations in physics. Many researchers use the theoretical knowledge of the critical point to obtain a series of good solution series of existential results. We consider the existential results of f solution in the cases of subcriticality, supercriticality, and criticality.

The above equations are very important in physics. Many researchers use the critical point theory to get a series of good results. We consider the existence of solutions for F in subcritical, supercritical and critical cases.<br>